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Sub-manifold and traveling wave solutions of Ito''s 5th-order mKdV equation
Keywords:Ito''s 5th-order mKdV equation, travelling wave solutions, sub-equations, dynamical system approach.
Abstract:
      In this paper, we study Ito''s 5th-order mKdV equation with the aid of symbolic computation system and by qualitative analysis of planar dynamical systems. We show that the corresponding higher-order ordinary differential equation of Ito''s 5th-order mKdV equation, for particular values of the parameter, possesses some sub-manifolds defined by planar dynamical systems. Some solitary wave solutions, kink and periodic wave solutions of the Ito''s 5th-order mKdV equation for these particular values of the parameter are obtained by studying the bifurcation and solutions of the corresponding planar dynamical systems.